Shifty eyes. A new mechanical model explains why the pupil wobbles for a while after the eye completes a scanning motion known as a saccade.

Shifty eyes. A new mechanical model explains why the pupil wobbles for a while after the eye completes a scanning motion known as a saccade. [Credit: iStock.com/mputsylo]×

When we read, our eyes don’t scan a page smoothly but perform a series of jumps, darting from one section of text to another. After each jump, known as a saccade, the pupil typically wobbles for a moment. Now researchers have developed a model for this wobble that involves only physical characteristics of the eyeball. The model could help scientists differentiate neurologically controlled eye movements from wobbles that are governed by the eye’s material properties.

Human eyes are rarely still. About three times per second, our gaze flits from one focal point to another as we take in the scene around us. These saccades are essential for perception, as only a small part of the retina is sensitive to color and details. They may also indicate changes in cognitive function, as eye motion can be affected by a concussion or a neurodegenerative disease, for example. But jump size and fixation time (the interval between saccades) vary appreciably from person to person and also depend on the visual task being performed. As a consequence of these variations, says vision expert Ralf Engbert of the University of Potsdam in Germany, “there is currently no broadly accepted standard for defining saccadic eye movement and, consequently, no generally accepted procedure for detecting saccades.”

The problem is further complicated by postsaccadic oscillations (PSOs), tiny wobbles of the pupil, lasting a few tens of milliseconds, that occur after a saccade. PSOs result from the pupil—the hole in the iris—moving back and forth relative to the iris's fixed outer edge. When the pupil briefly moves right-of-center, for example, the iris tissue to the right is slightly compressed, and the tissue to the left is slightly stretched. (Of course, the pupil is empty space, so it doesn’t actually push on the tissue; it’s motion is a result of the iris’s inertia.)

Since PSOs can last a substantial fraction of the fixation time, which varies from about 180 to 330 milliseconds (ms), they can interfere with the definition and detection of saccades. Researchers have generally taken them to be a consequence of the eyes’ mechanical properties, rather than a neurologically caused motion, but they have not proposed a quantitative model that reproduces the phenomenon. Biophysicist Sebastián Bouzat of the Bariloche Atomic Center in Argentina and his colleagues have now developed a model that replicates and quantitatively defines PSOs, making it possible to distinguish them from saccades.

The team’s theoretical, one-dimensional model includes two forces affecting the pupil as it responds to a saccade—a spring-like connection to the eyeball that tends to center the pupil and viscosity, from the fluid inside the eyeball, that retards its motion. Using a numerical method to solve the equations of motion for this model, the researchers created a saccade by abruptly moving the eyeball sideways, with the jump taking between 10 and 100 ms, depending on the size of the sideways shift. The pupil took a couple of milliseconds to start moving, then caught up and moved ahead of the eyeball’s center. When the jump ended, the pupil wobbled back and forth for up to 40 ms before coming to a standstill.

The PSO amplitude grew with increasing jump size for smaller jumps, then reached a peak and slowly decreased for larger jumps. Transforming their model results into predictions for real eyeballs, the researchers found that the largest PSO amplitude, roughly 1°, occurred for a gaze shift of around 5–8°, which corresponds roughly to moving your focus the distance of four keys on a keyboard. The predictions agree with data from eye tracking experiments [1].

The model confirms that PSOs arise from the mechanical properties of the eye, says Bouzat. “The inner part of the iris keeps on moving for a while after the eyeball stops because everything is like jelly inside the eye.”

Ignace Hooge, who studies the links between eye movement and cognition at Utrecht University in the Netherlands, says that in addition to providing a detailed description of how the eye behaves during and after saccades, the model has potential as a tool to correctly distinguish neurological eyeball motions from simple eye jelly wobbles in eye tracking experiments.

Engbert calls the model an important step toward understanding how saccadic behavior varies among individuals. The difference in average fixation time for disparate cognitive tasks, like reading or searching a scene, can be as little as 5 ms, he says, so even a small amount of uncertainty in defining the start and finish of saccades can make a critical difference in measuring them accurately.